Question

A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space along with the associated value of X.

S: FFF SFF FSF FFS FSS SFS SSF SSS X:

Answer 1

`\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}`

Explanation:

Given

`S_S = \{FFF, SFF, FSF, FFS, FSS, SFS, SSF, SSS\}`

`X \to` Number of beams failed by shear

Required

List each outcome and the value of X

To do this, we simply count the occurrence of S in each outcome.

This is tabulated as follows:

`\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}`